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A new lawsuit accuses President Trump, his company and three of his children of using the Trump name to entice vulnerable people to invest in sham business opportunities.

Filed in federal court in Manhattan on Monday, the lawsuit comes just days before the midterm elections, raising questions about whether its timing is politically motivated. It is being underwritten by a nonprofit whose chairman has been a donor to Democratic candidates.

The allegations take aim at the heart of Mr. Trump’s personal narrative that he is a successful deal-maker who built a durable business, charging he and his family lent their name to a series of scams.

The 160-page complaint alleges that Mr. Trump and his family received secret payments from three business entities in exchange for promoting them as legitimate opportunities, when in reality they were get-rich-quick schemes that harmed investors, many of whom were unsophisticated and struggling financially.

Those business entities were ACN, a telecommunications marketing company that paid Mr. Trump millions of dollars to endorse its products; the Trump Network, a vitamin marketing enterprise; and the Trump Institute, which the suit said offered “extravagantly priced multi day training seminars” on Mr. Trump’s real estate “secrets.”

The four plaintiffs, who were identified only with pseudonyms like Jane Doe, depict the Trump Organization as a racketeering enterprise that defrauded thousands of people for years as the president turned from construction to licensing his name for profit. The suit also names Donald Trump Jr., Ivanka Trump and Eric Trump as defendants.

A lawyer for the Trump Organization, Alan Garten, said the allegations were completely meritless and relate to events that happened a decade ago. “This is clearly just another effort by opponents of the President to use the court system to advance a political agenda,” the spokesman said. He noted the plaintiffs’ lawyers have longstanding and deep ties to the Democratic Party and waited to file until just before the election. “Their motivations are as plain as day.”

A White House spokeswoman for Mr. Trump did not immediately respond to requests for comment.

But the new suit alleges “a pattern of racketeering activity” involving three other organizations. Roberta A. Kaplan and Andrew G. Celli Jr., two lawyers for the plaintiffs, said in a statement that they were not aware of “any prior case against the Trumps alleging consumer fraud on this scale.”

“This case connects the dots at the Trump Organization and involves systematic fraud that spanned more than a decade, involved multiple Trump businesses and caused tremendous harm to thousands of hardworking Americans,” the statement said.

Asked about the suit’s timing, Ms. Kaplan and Mr. Celli said their firms — Kaplan, Hecker & Fink and Emery, Celli, Brinckerhoff & Abady — had conducted a lengthy investigation and the plaintiffs were eager to file. “The case is being brought now because it is ready now,” the lawyers said.

The lawyers said a nonprofit organization, the Tesseract Research Center, was funding the lawsuit by paying attorney’s fees and costs.

Morris Pearl, the Democratic donor who is the nonprofit’s chairman, said in a statement that his organization hoped to draw attention to the challenges faced by people who sustain losses but cannot seek redress through the courts “ because of the extreme wealth and power on the other side.”

The lawyers said they were asking the court to allow the plaintiffs to proceed using pseudonyms because of “serious and legitimate security concerns given the heated political environment.” The lawyers also declined to make their clients available for interviews.

The four plaintiffs each invested in ACN after watching promotional videos featuring Mr. Trump.

According to the lawsuit, ACN required investors to pay $499 to sign up to sell its products, like a videophone and other services, with the promise of additional profits if they recruited others to join.

Mr. Trump described the phone in an ACN news release as “amazing” but failed to disclose he was being “paid lavishly for his endorsement,” the suit says.

One plaintiff, a hospice worker from California identified as “Jane Doe,” decided to join ACN in 2014 after attending a recruitment meeting at a Los Angeles hotel where she listened to speakers and watched Mr. Trump on video extol the investment opportunity.

For her, the video was the “turning point,” the lawsuit said.

“Doe believed that Trump had her best interests at heart,” the suit said.

Jane Doe then signed up for a larger ACN meeting in Palm Springs, Calif., which cost almost $1,500, and she later spent thousands more traveling to conventions in Cleveland and Detroit, according to the suit.

In the end, she earned $38 — the only income she would ever receive from the company, the suit said.